Mr Coulson denies he was aware of phone hacking while he was at the newspaper.

And Conservative minister Alan Duncan said Labour was mounting a concerted campaign against the government.

The News of the World's royal editor, Clive Goodman, was jailed for conspiracy to access phone messages in 2007, but the paper insists it was an isolated case.

Last year, the Metropolitan Police chose not to launch an investigation into claims, made by the Guardian newspaper, that a host of public figures - including former deputy PM Lord Prescott - had had their messages hacked by journalists there.

At the time, it said the evidence did not warrant it and suggested Lord Prescott's phone had not been tapped.

Following the latest concerns expressed by Labour figures, BBC political correspondent Gary O'Donoghue said: "Asked whether or not his position was in doubt, one very senior source in the government said Andy is going nowhere."

Our correspondent said there is "some political advantage to the Labour party to stir up as much trouble as possible for Andy Coulson" because he is "central to the Downing Street operation" since he is "very close to David Cameron and extremely important to what he does".

He said No 10 "totally and utterly rejected the idea that he allowed anyone [or] asked anyone to hack into any phones".

The Downing St denials come after Lord Prescott said he would go to court to find out if his phone was tapped. And ex-Home Secretary Alan Johnson said last year's police probe could be reviewed.

Meanwhile, former culture secretary Tessa Jowell told the Independent: "I know I was tapped 28 times by May 2006 because the police told me.

"I had a call when I was on holiday in August 2006 from the Met to say that I had been tapped, but they asked me to do nothing except increase the security on my phone."

Calls for further action by Labour politicians were prompted by allegations in the New York Times about the extent of phone hacking which went on at the News of The World.

'Extreme scepticism'

Former News of the World employee Sean Hoare, one of the sources for the New York Times' allegations, told the BBC that phone tapping was "endemic" within the industry and he had been personally "requested" to do so by his then editor, Mr Coulson.

"He was well aware that the practice exists," he told Radio 4's PM programme.

But the newspaper said the claims by Mr Hoare should be treated with "extreme scepticism".

However, former News of the World sport reporter Matt Driscoll told the BBC he thought it was "unconceivable" that Mr Coulson would have been unaware of phone hacking practices when he was at the paper because "he would be a part of all the big stories that were being made by the paper".

Lord Prescott said he wanted to "find the truth" about whether he had been targeted by journalists and would seek a judicial review unless the police supplied him with information in its possession by next week.

Image caption
Former minister Tessa Jowell says her phone was tapped at least 28 times

Fellow Labour MP Chris Bryant believes he was also targeted but said he had not been informed by the police. Solicitors acting for the MP said they would challenge the Met's decision in court.

Separately, shadow home secretary Alan Johnson said there was a case for Her Majesty's Inspectorate of Constabulary to review the Met's handling of the case and he would ask to see Home Office files on the allegations.

However, Conservative MP and government minister Alan Duncan, speaking on Radio 4's Any Questions, said comments by Labour MPs were part of a concerted campaign to attack the government.

"Things are getting ramped up in the media based on rumour and innuendo and, as in the William Hague case, I don't think it's acceptable in this case. And unless anybody comes forward with any clear evidence this is not something that should be pursued," he said.

Mr Coulson resigned after Mr Goodman - and a private investigator - were jailed in 2007, saying he took responsibility for the incident while insisting he was not aware of what the journalist had done and never sanctioned his activities.

'No new evidence'

He told a Commons committee which looked into the allegations last year that he never "used or condoned" phone tapping and was deceived by the journalist concerned.

While critical of the conduct of the News of The World's journalists, the Culture Committee found no evidence that Mr Coulson either approved phone-hacking by his paper, or was aware it was taking place.

The News of the World said the New York Times allegations "contained no new evidence".

"It relies on unsubstantiated allegations from unnamed sources or claims from disgruntled former employees that should be treated with extreme scepticism given the reasons for departures from this newspaper," it said in a statement.

"We reject absolutely any suggestion there was widespread culture of wrongdoing at the News of the World."